On the dimension of additive sets

P. Candela, and H. A. Helfgott. "On the dimension of additive sets." Acta Arithmetica 167.1 (2015): 91-100. <http://eudml.org/doc/278941>.

@article{P2015,
abstract = {We study the relations between several notions of dimension for an additive set, some of which are well-known and some of which are more recent, appearing for instance in work of Schoen and Shkredov. We obtain bounds for the ratios between these dimensions by improving an inequality of Lev and Yuster, and we show that these bounds are asymptotically sharp, using in particular the existence of large dissociated subsets of \{0,1\}ⁿ ⊂ ℤⁿ.},
author = {P. Candela, H. A. Helfgott},
journal = {Acta Arithmetica},
keywords = {additive dimension; dissociated sets},
language = {eng},
number = {1},
pages = {91-100},
title = {On the dimension of additive sets},
url = {http://eudml.org/doc/278941},
volume = {167},
year = {2015},
}

TY - JOUR
AU - P. Candela
AU - H. A. Helfgott
TI - On the dimension of additive sets
JO - Acta Arithmetica
PY - 2015
VL - 167
IS - 1
SP - 91
EP - 100
AB - We study the relations between several notions of dimension for an additive set, some of which are well-known and some of which are more recent, appearing for instance in work of Schoen and Shkredov. We obtain bounds for the ratios between these dimensions by improving an inequality of Lev and Yuster, and we show that these bounds are asymptotically sharp, using in particular the existence of large dissociated subsets of {0,1}ⁿ ⊂ ℤⁿ.
LA - eng
KW - additive dimension; dissociated sets
UR - http://eudml.org/doc/278941
ER -